I vs. Me

Hello,

I was told the rule is: if you can remove the other subject and "I" or "me" still works, you have the right form. So:

"Please let Elizabeth or me know if you have any questions."

This is correct because "Please let me know if you have any questions." still works.

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"Please let Elizabeth or I know if you have any questions."

This is incorrect because "Please let I know if you have any questions" does not work.

Is this rule right?

Thank you very much.